Symmetric research joint ventures: Cooperative substitutes and complements

We introduce the concepts of cooperative substitutes and complements, and use them to explain when all firms in a research joint venture will choose equal levels of R&D. We show that the second-order conditions for a symmetric optimum take a particularly simple form, ruling out both excessive cooperative substitutability and excessive cooperative complementarity, and nesting conditions already derived in the literature. Finally we apply our results to the comparison between cooperative and non-cooperative R&D, and show in an important special case that asymmetric outcomes are only optimal for a very limited range of parameter values.